Valence and inner hole responses via the208Pb(d→,t)207Pbreaction atEd=200MeVand form factor dependence

The study of the ${}^{208}\mathrm{Pb}(\stackrel{\ensuremath{\rightarrow}}{d}{,t)}^{207}\mathrm{Pb}$ reaction at ${E}_{d}=200\mathrm{MeV}$ has been extended up to typically ${E}_{x}=40\mathrm{MeV}$ in ${}^{207}\mathrm{Pb}$ using a polarized beam with both vector and tensor components. Two-step pickup reactions involving low multipolarity collective transitions have been evaluated for the first time via systematic coupled channel calculations, allowing a new approach of the background determination. The $(\stackrel{\ensuremath{\rightarrow}}{d},t)$ observables corresponding to the overlapping ${1h}_{11/2},$ ${1g}_{7/2},$ and ${1g}_{9/2}$ inner hole responses have been analyzed up to ${E}_{x}=25\mathrm{MeV}$ via a least squares fit procedure. Necessary input values were deduced for hole states of interest from finite range distorted wave (DWBA) calculations. The optical parameters and the range function were those successfully used in a previous survey of valence state observables. The highest $j$ transitions are enhanced in the reaction and analyzing powers exhibit strongly characteristic features for ${j}_{\ensuremath{-}}=l\ensuremath{-}1/2$ versus ${j}_{+}=l+1/2$ states. We have calculated for the first time the separation energy dependence of $\mathrm{nlj}$ transition observables, taking into account the form factor modifications induced by the hole coupling with surface vibrations. The calculations have been performed in the framework of the quasiparticle-phonon model (QPM). This analysis (QPMFF) predicts a large variation of differential cross sections with excitation energy of the hole fragments, while angular distribution shapes remain quite stable. The strength distributions resulting of the QPMFF analysis and of a standard analysis using DWBA observables calculated at the centroid energies are systematically compared. As a general rule, the QPMFF analysis increases the strength concentration toward lower excitation energy. The corresponding ${1h}_{11/2},$ ${1g}_{7/2},$ and the tentative ${1g}_{9/2}$ strength distributions are compared and discussed with the available theoretical calculations. In particular, the narrower spreading widths deduced via the QPMFF analysis are quite well predicted by the calculation of spectral functions in a modified mean field. The ${1i}_{13/2}$ and ${1h}_{9/2}$ valence strength distributions are revisited along this new approach and found to be in fair agreement with the fragmentation predicted by the QPM, which is not the case of inner hole strength distributions.